Algebra Examples

$x (4 x + 5) + 3 (2 x^{2} - 4 x + 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x (4 x) + x \cdot 5 + 3 (2 x^{2} - 4 x + 1)$

Step 1.2

Rewrite using the commutative property of multiplication.

$4 x \cdot x + x \cdot 5 + 3 (2 x^{2} - 4 x + 1)$

Step 1.3

Move $5$ to the left of $x$ .

$4 x \cdot x + 5 \cdot x + 3 (2 x^{2} - 4 x + 1)$

Step 1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.4.1

Move $x$ .

$4 (x \cdot x) + 5 \cdot x + 3 (2 x^{2} - 4 x + 1)$

Step 1.4.2

Multiply $x$ by $x$ .

$4 x^{2} + 5 \cdot x + 3 (2 x^{2} - 4 x + 1)$

$4 x^{2} + 5 x + 3 (2 x^{2} - 4 x + 1)$

Step 1.5

Apply the distributive property.

$4 x^{2} + 5 x + 3 (2 x^{2}) + 3 (- 4 x) + 3 \cdot 1$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $2$ by $3$ .

$4 x^{2} + 5 x + 6 x^{2} + 3 (- 4 x) + 3 \cdot 1$

Step 1.6.2

Multiply $- 4$ by $3$ .

$4 x^{2} + 5 x + 6 x^{2} - 12 x + 3 \cdot 1$

Step 1.6.3

Multiply $3$ by $1$ .

$4 x^{2} + 5 x + 6 x^{2} - 12 x + 3$

Step 2

Simplify by adding terms.

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Step 2.1

Add $4 x^{2}$ and $6 x^{2}$ .

$10 x^{2} + 5 x - 12 x + 3$

Step 2.2

Subtract $12 x$ from $5 x$ .

$10 x^{2} - 7 x + 3$